QJEEM19Maee8d: JEE Main 2019 Mathematics - Class 11 JEEM19Maee8d Solution: Let z be a complex number such that

Question

Verified Solution • 2025–26 Session moderate

Let z be a complex number such that |z| + z = 3 + i (where i =

\sqrt{- 1}

). Then |z| is equal to :

Accepted Answer

| z | + z = 3 + i

z = 3 - | z | + i

Let

3 - | z | = a \Rightarrow | z | = (3 - a)

\Rightarrow z = a + i \Rightarrow | z | = \sqrt{a^{2} + 1}

\Rightarrow 9 + a^{2} - 6 a = a^{2} + 1 \Rightarrow a = \frac{8}{6} = \frac{4}{3}

\Rightarrow | z | = 3 - \frac{4}{3} = \frac{5}{3}

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